Green Functions in Finite 基本步骤 V2G(r;r)=-26(r-r) Xlr Vdu(r ×G(r;r) // u(r)V'G(r; r)-G(r; rVu(r) dr
Concept of Green Functions Green Functions in Time-Independent Problems Green Ftns of 3D Holmholtz eq. Superposition Principles in Infinite Space Green Functions in Finite Space: Definition Ä Ú½ ∇2G(r; r 0 ) = − 1 ε0 δ(r − r 0 ) ×u(r) ∇2u(r) = − 1 ε0 ρ(r) ×G(r; r 0 ) ZZZ V u(r)∇2G(r; r 0 ) − G(r; r 0 )∇2u(r) dr = − 1 ε0 ZZZ V u(r)δ(r − r 0 ) − G(r; r 0 )ρ(r) dr C. S. Wu 1Êù Green¼ê()
Green Functions in Finite 基本步骤 V2G(r;r)=-26(r-r) Xlr Vdu(r 多E0 ×G(r;r) lu(r)VG(r; r)-G(r: r)Vu(r).d2
Concept of Green Functions Green Functions in Time-Independent Problems Green Ftns of 3D Holmholtz eq. Superposition Principles in Infinite Space Green Functions in Finite Space: Definition Ä Ú½ ∇2G(r; r 0 ) = − 1 ε0 δ(r − r 0 ) ×u(r) ∇2u(r) = − 1 ε0 ρ(r) ×G(r; r 0 ) ZZ Σ u(r)∇G(r; r 0 ) − G(r; r 0 )∇u(r) · dΣ = − 1 ε0 ZZZ V u(r)δ(r − r 0 ) − G(r; r 0 )ρ(r) dr C. S. Wu 1Êù Green¼ê()
Green Functions in Finite 基本步骤 V2G(r;r)=--6(r-r)×(r) p(r) G(r;r) u(r)VG(r; r)-G(r: r)Vu(r).de (r) G(r; rp(r)d
Concept of Green Functions Green Functions in Time-Independent Problems Green Ftns of 3D Holmholtz eq. Superposition Principles in Infinite Space Green Functions in Finite Space: Definition Ä Ú½ ∇2G(r; r 0 ) = − 1 ε0 δ(r − r 0 ) ×u(r) ∇2u(r) = − 1 ε0 ρ(r) ×G(r; r 0 ) ZZ Σ u(r)∇G(r; r 0 ) − G(r; r 0 )∇u(r) · dΣ = − 1 ε0 u(r 0 ) − ZZZ V G(r; r 0 )ρ(r)dr C. S. Wu 1Êù Green¼ê()
Green Functions in Finite ulr G(r; rp(rdr / u(r)VG(r; r)G(r; r)Vu(r) d2
Concept of Green Functions Green Functions in Time-Independent Problems Green Ftns of 3D Holmholtz eq. Superposition Principles in Infinite Space Green Functions in Finite Space: Definition u(r 0 ) = ZZZ V G(r; r 0 )ρ(r)dr −ε0 ZZ Σ u(r)∇G(r; r 0 )−G(r; r 0 )∇u(r) ·dΣ ¡È©¥µ 1¥§u(r)3>.¡Σþê®(> .^) 1¥§∇u(r)3>.¡þê ¤±7LéG(r; r 0 )\þàg>.^ G(r; r 0 ) Σ = 0 C. S. Wu 1Êù Green¼ê()
Green Functions in Finite ulr G(r; rp(rdr -Eo// u(r)VG(r r' G(; r')Vu(r).d2 面积分中 第一项中,u()在边界面∑上的数值已知(边 界条件) 第二项中,V(7)在边界面上的数值未知
Concept of Green Functions Green Functions in Time-Independent Problems Green Ftns of 3D Holmholtz eq. Superposition Principles in Infinite Space Green Functions in Finite Space: Definition u(r 0 ) = ZZZ V G(r; r 0 )ρ(r)dr −ε0 ZZ Σ u(r)∇G(r; r 0 )−G(r; r 0 )∇u(r) ·dΣ ¡È©¥µ 1¥§u(r)3>.¡Σþê®(> .^) 1¥§∇u(r)3>.¡þê ¤±7LéG(r; r 0 )\þàg>.^ G(r; r 0 ) Σ = 0 C. S. Wu 1Êù Green¼ê()